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Please answer the following question with explanation

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Asked by Deepak 11th September 2018, 12:54 PM
Answered by Expert
Answer:
Figure shows the cross section of wire of radius R.
In order to find the current passing through region between radius R/3 and outer radius R/2,
let us consider a region of inner radius r and thickness dr as shown in figure.
Current dI passing through the above mentioned region is given by,   dI = J(r)×A(r) ..................(1)
where J(r) is given current density, A(r) is area of the considered region.
 
begin mathsize 12px style d I space equals space J left parenthesis r right parenthesis cross times A left parenthesis r right parenthesis space equals space a r squared space cross times space 2 pi cross times r cross times d r space equals space 2 pi cross times a cross times r cubed cross times d r space.................. left parenthesis 2 right parenthesis end style
Current I passing through region between inner radius R/3 and outer radius R/5 is , begin mathsize 12px style I space equals space integral d I space equals space 2 pi cross times a cross times integral subscript bevelled R over 3 end subscript superscript bevelled R over 2 end superscript r cubed d r space almost equal to space pi over 40 cross times a cross times R to the power of 4 end style
Answered by Expert 11th September 2018, 4:59 PM
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